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3 years ago

Which of the following are roots of the polynomial function? Check all that apply f(x) = x^3 + 3x^2 - 9x + 5

Mathematics

1 answer:

lakkis [162]3 years ago

8 0

Answer:

x = 1 or x = -5

Step-by-step explanation:

Solve for x:

x^3 + 3 x^2 - 9 x + 5 = 0

The left hand side factors into a product with two terms:

(x - 1)^2 (x + 5) = 0

Split into two equations:

(x - 1)^2 = 0 or x + 5 = 0

Take the square root of both sides:

x - 1 = 0 or x + 5 = 0

Add 1 to both sides:

x = 1 or x + 5 = 0

Subtract 5 from both sides:

Answer: x = 1 or x = -5

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An airline is planning its staffing needs for the next year. If a new route is approved, it will hire 837 new employees. If a n

dusya [7]

Considering a discrete distribution, it is found that the expected number of new employees to be hired by the airline is of 446.16.

<h3>What is the mean of a discrete distribution?</h3>

The expected value of a discrete distribution is given by the <u>sum of each outcome multiplied by it's respective probability</u>.

In this problem, considering the situation described in the text, the distribution is given by:

P(X = 837) = 0.37.

P(X = 199) = 0.63.

Hence, the expected value is given by:

E(X) = 0.37(867) + 0.63(199) = 446.16.

More can be learned about discrete distributions at brainly.com/question/24855677

6 0

2 years ago

Which equivalent fractions can you use to find the sum of 2/8 + 3/9?

sattari [20]

You can you 72 which would make 2/8 18/72 and 3/9 24/72 which makes the sum 42/72.

7 0

3 years ago

Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do n

aliya0001 [1]

Answer:

$f(x)=\sum_{n=1}^{\infty}(-1)^{(n-1)}2^{n}\dfrac{x^n}{n}$

Step-by-step explanation:

The Maclaurin series of a function f(x) is the Taylor series of the function of the series around zero which is given by

$f(x)=f(0)+f^{\prime}(0)x+f^{\prime \prime}(0)\dfrac{x^2}{2!}+ ...+f^{(n)}(0)\dfrac{x^n}{n!}+...$

We first compute the n-th derivative of $f(x)=\ln(1+2x)$ , note that

$f^{\prime}(x)= 2 \cdot (1+2x)^{-1}\\f^{\prime \prime}(x)= 2^2\cdot (-1) \cdot (1+2x)^{-2}\\f^{\prime \prime}(x)= 2^3\cdot (-1)^2\cdot 2 \cdot (1+2x)^{-3}\\...\\\\f^{n}(x)= 2^n\cdot (-1)^{(n-1)}\cdot (n-1)! \cdot (1+2x)^{-n}\\$

Now, if we compute the n-th derivative at 0 we get

$f(0)=\ln(1+2\cdot 0)=\ln(1)=0\\\\f^{\prime}(0)=2 \cdot 1 =2\\\\f^{(2)}(0)=2^{2}\cdot(-1)\\\\f^{(3)}(0)=2^{3}\cdot (-1)^2\cdot 2\\\\...\\\\f^{(n)}(0)=2^n\cdot(-1)^{(n-1)}\cdot (n-1)!$

and so the Maclaurin series for f(x)=ln(1+2x) is given by

$f(x)=0+2x-2^2\dfrac{x^2}{2!}+2^3\cdot 2! \dfrac{x^3}{3!}+...+(-1)^{(n-1)}(n-1)!\cdot 2^n\dfrac{x^n}{n!}+...\\\\= 0 + 2x -2^2 \dfrac{x^2}{2!}+2^3\dfrac{x^3}{3!}+...+(-1)^{(n-1)}2^{n}\dfrac{x^n}{n}+...\\\\=\sum_{n=1}^{\infty}(-1)^{(n-1)}2^n\dfrac{x^n}{n}$

3 0

3 years ago

If a student did not travel to a Spanish-speaking country, how many times more likely is it that the student did not take Spanis

olasank [31]

Answer:

It is 2.2 times as likely.

3 0

3 years ago

a group of 31 friends gets together to play a sport. first people must be divided into teams. each team has to exactly 4 players

azamat

We have the following values:
Total people: 31
People per team: 4
The number of teams will then be:
N = (31) / (4)
N = 7.75
Round to the previous whole number.
N = 7
There are 7 teams.
Answer:
they can make about 7 teams.

3 0

4 years ago